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arXiv:submit/2577769 [cs.ET] 19 Feb 2019

1

Evaluation, Modeling and Optimization of

Coverage Enhancement Methods of NB-IoT

Sahithya Ravi∗†, Pouria Zand∗, Mohieddine El Soussi∗and Majid Nabi† ∗ Holst

Centre / IMEC-NL, Eindhoven, The Netherlands

†Electrical Engineering Department, Eindhoven University of Technology,

Eindhoven, The Netherlands

Email: Sahithya.ravi@imec.nl, pouria.zand@imec.nl,

mohieddine.elsoussi@imec.nl, m.nabi@tue.nl

Abstract

Narrowband Internet of Things (NB-IoT) is a new Low Power Wide Area Network (LPWAN)

technology released by 3GPP. The primary goals of NB-IoT are improved coverage, massive capacity,

low cost, and long battery life. In order to improve coverage, NB-IoT has promising solutions, such

as increasing transmission repetitions, decreasing bandwidth, and adapting the Modulation and Coding

Scheme (MCS). In this paper, we present an implementation of coverage enhancement features of NB-

IoT in NS-3, an end-to-end network simulator. The resource allocation and link adaptation in NS-3 are

modiﬁed to comply with the new features of NB-IoT. Using the developed simulation framework, the

inﬂuence of the new features on network reliability and latency is evaluated. Furthermore, an optimal

hybrid link adaptation strategy based on all three features is proposed. To achieve this, we formulate an

optimization problem that has an objective function based on latency, and constraint based on the Signal

to Noise Ratio (SNR). Then, we propose several algorithms to minimize latency and compare them with

respect to accuracy and speed. The best hybrid solution is chosen and implemented in the NS-3 simulator

by which the latency formulation is veriﬁed. The numerical results show that the proposed optimization

algorithm for hybrid link adaptation is eight times faster than the exhaustive search approach and yields

similar latency.

Index Terms

NB-IoT, Coverage enhancement, Link adaptation, Optimization, NS-3.

I. INT RO DUC TION

The Internet of Things (IoT) refers to the idea of connecting everyday objects to the Internet,

enabling them to send and receive data. There is a wide range of applications for IoT in the areas

of smart cities, asset tracking, smart agriculture, health monitoring and so on. The IoT landscape

consists of wireless technologies that operate in licensed or unlicensed bands, achieving ranges

from less than ten meters up to tens of kilometers with data rates from a few bps to Mbps.

Low Power Wide Area Network (LPWAN) targets low-power and long-range applications with

data rates from 10 bps up to a few kbps. Narrowband-IoT (NB-IoT) [1] is a licensed LPWAN

technology, which was standardized in 2016 by the Third Generation Partnership Project (3GPP).

NB-IoT can be deployed in Global System for Mobile Communications (GSM) or Long-Term

Evolution (LTE) networks, and can co-exist with LTE. NB-IoT uses a new physical layer design

that facilitates a wide range of IoT applications in the licensed spectrum that require long range,

deep indoor penetration, low cost, low data rate, low power consumption, and massive capacity

[2].

Among the aforementioned requirements, this paper focuses on uplink coverage enhancement.

Many solutions are proposed in the standard to achieve coverage enhancement for NB-IoT. The

ﬁrst solution, referred as tones, is to reduce the bandwidth and to perform resource allocation

based on tones (or subcarriers) instead of Resource Blocks (RBs). A lower number of tones

enables the User Equipment (UE) to transmit in a narrower bandwidth. The second solution

is repetitions, which refers to repeating the data transmission multiple times. The last solution

is Modulation and Coding Scheme (MCS), which is already used in LTE to achieve better

coverage [3]. Considering the new features of tones and repetitions, uplink link adaptation needs

to be performed in three dimensions - using tones, repetitions and MCS. In this paper, coverage

enhancement features of NB-IoT are implemented in NS-3 simulator and the effect of each one

of these features on reliability and latency is evaluated and analyzed. Furthermore, a hybrid link

adaptation considering tones, repetitions and MCS is provided so that the latency per user is

minimal and good reliability is achieved. Different techniques for optimization are tried out and

compared in terms of execution time and accuracy.

A. Background

NB-IoT has a bandwidth of 180 kHz which corresponds to one RB of LTE. In the uplink, the

bandwidth of 180 kHz can be distributed among 12 subcarriers or tones with 15 kHz spacing,

2

or 48 subcarriers with 3.75 kHz spacing. The subframe duration for 3.75 kHz spacing is 4 ms,

which is four times that of 15 kHz spacing [4].

NB-IoT supports single-tone and multi-tone communication in the uplink. In case of multi-

tone, there are three options with 12, 6 and 3 subcarriers. In case of single-tone, there is only 1

subcarrier with either 15 kHz or 3.75 kHz spacing. A higher number of tones is used to provide

higher data rates for devices in normal coverage, while a lower number of tones is used for

devices that need extended coverage. A single packet of a ﬁxed size is transmitted over 1 ms in

case of 12 tones, 2 ms in case of 6 tones, 4 ms in case of 3 tones, 8 ms in case of 1 tone (15

kHz spacing) and 32 ms in case of 1 tone (3.75 kHz spacing) [5].

MCS is the feature that inﬂuences the type of modulation and code rate. MCS is directly

proportional to the code rate and Transport Block Size (TBS) and can take values from 0 to 12

[6]. As the channel quality deteriorates, the MCS becomes lower and thus the code rate and TBS

become lower. MCS, tones and repetitions are assigned based on channel quality. Repetitions

of uplink data can take values of 1, 2, 4, 8, 16, 32, 64 and 128. When channel quality is poor,

tones and MCS are decreased and repetitions are increased.

B. State-of-the-art

Constituting a relatively new technology, there are a lot of open issues that need to be

investigated for NB-IoT, such as performance analysis, link adaptation, design optimization,

and co-existence with other technologies. The performance of NB-IoT with respect to coverage,

capacity, and co-existence with LTE has been studied in, for instance, [7], [8], [9] and [10]. The

focus of our paper is towards implementation and evaluation of coverage enhancement techniques

and link adaptation based on coverage enhancement methods.

NS-3 is an open source network simulator commonly used for evaluating wireless technologies

such as LTE. The NS-3 LTE module is well-tested and can be used as a base for developing

the NB-IoT module. The work on NB-IoT module in NS-3 began in [11], in which the authors

modiﬁed downlink signaling trafﬁc such as the Master Information Block (MIB) and the System

Information Block (SIB) to comply with NB-IoT speciﬁcation. In [12], the authors restricted the

bandwidth to one Resource Block (RB) which is 180 kHz and separated the control and data

channels. This paper aims to extend [12], by modifying the resolution of resources from RB to

subcarriers, implementing the single and multi-tone uplink features, and including repetitions in

the uplink.

3

With respect to uplink link adaptation of NB-IoT, the authors of [13] propose a 2D link

adaptation strategy based on MCS and repetitions and use link-level simulations to evaluate the

performance of their solution. In this paper, however, we use a system and network level simulator

(NS-3) to evaluate our solution through end-to-end simulations. Further, they do not take tones

into account, which is an important dimension to be considered for link adaptation. Furthermore,

they do not consider a hybrid solution instead they ﬁx one parameter while varying the other.

In [14], the authors derive analytic equations that model the impact of repetitions, tones and

MCS. They also propose an exhaustive search method that searches all possible combinations

of repetitions, tones, and MCS to minimize the transmission latency. However, their analysis

of the coverage enhancement features is entirely based on analytic models and has not been

veriﬁed using network simulations. This paper ﬁrst performs the hybrid link adaptation using

analytic approaches and compares the outcome to the results of end-to-end simulations to verify

the accuracy of the solution. Furthermore, instead of an exhaustive search method, we propose

a closed-form solution that achieves the optimum result with lower complexity.

II. NB-IOTIMPLEM ENTATION A ND EVALUATION

The NB-IoT module of NS-3 is built using the existing LTE module. The LTE module in

NS-3 includes aspects such as radio resource management (RRC), physical layer error model

[15], QoS-aware packet scheduling, inter-cell interference coordination, and dynamic spectrum

access. Based on the LTE module in NS-3, the authors of [12] implemented the basic features

for eMTC and NB-IoT modules. Based on the NB-IoT module described in [12], we implement

the uplink coverage enhancement features.

A. Implementation of tones and repetitions

In order to implement tones, modiﬁcations are made in both time domain (extending a packet

according to tone) and frequency domain (transmitting over a narrower bandwidth). It is know

that reducing bandwidth improves the Signal-to-Noise Ratio (SNR) as the transmitted power

spectral density increases. In order to support bandwidth lower than 180 kHz (1 RB), the existing

resource allocation is modiﬁed from RB-based allocation to subcarrier-based allocation.

In order to implement repetitions, major modiﬁcations are made in the time domain (repeating

a data packet). Whenever repetition is used, the subsequent repetitions of the same data are

aggregated at the eNodeB. Hence, the resulting SNR after the aggregation is the sum of the

4

SINR (SRS) Error

model

MCS=12

tone =12

Repetition=1

Adapt

MCS/tone/

repetition

BLER < 0.1

Assign

MCS/tone/

repetition

Yes

No

Fig. 1: The link adaptation mechanism.

(a) Assigned value vs zone (b) Achieved PDR vs zone (c) Achieved delay vs zone

Fig. 2: Performance of link adaptation in open area and urban scenarios.

SNRs of each received repetition. Therefore, repetition of two results in an improvement of

approximately 3dB in SNR [14]. In order to achieve this behavior, we have modiﬁed the physical

layer of the base station in NS-3 to aggregate all the repetitions, and use the ﬁnal sum of SNR

as input to the error model described in [15].

B. Implementation of link adaptation

Link adaptation is performed based on the SNR received from the Secondary Reference Signal

(SRS). SRS is a signal that is sent periodically by the UE. Fig. 1 shows the link adaptation

mechanism. The SNR received from the SRS is provided as input to the error model of NS-3 to

ﬁnd the Block Error Rate (BLER) corresponding to the SNR [15]. If the BLER is less than the

target BLER of 0.1, the MCS and tone are ﬁxed to the highest value (12 tones) and repetition is

ﬁxed to the lowest value (1 repetition). If the target BLER is not met, MCS, tone and repetition

are adapted and re-evaluated using the error model. This process is repeated until a BLER of 0.1

5

or less is reached. The ﬁnal value of the MCS, tone or repetition that resulted in the BLER of

0.1 or less is assigned to the UE. Three independent methods of link adaptation are performed:

1) MCS is adapted based on SNR (repetitions are ﬁxed to 1 and tones are ﬁxed to 12).

2) Tones are adapted based on SNR (repetitions are ﬁxed to 1 and MCS is ﬁxed to 12).

3) Repetitions are adapted based on SNR (MCS is ﬁxed to 12 and tones are ﬁxed to 12).

C. Evaluation

The three link adaptation strategies are evaluated using NS-3. The performance evaluation is

carried out for random deployment scenarios. We consider two scenarios: open area and urban.

In open area, the eNodeB is located in the center and UE’s are arranged in a random fashion at

different distances from the eNodeB up to a distance of 25 km. Note that as distance increases,

the SNR becomes lower. In urban scenario, we include buildings and we assume that 80-90%

of the users are located inside the buildings. For a given distance, SNR is relatively lower inside

a building than outside. The simulation parameters for these scenarios are shown in Table I.

In each scenario, the nodes are grouped among different zones. There are 16 zones which

start at different distance from the eNodeB as indicated by the “Zone start” ﬁeld in Table I.

The zones are separated by three different intervals indicated as “Zone width” ﬁeld in Table I.

Fig. 2 shows the results for open area and urban scenarios. Fig. 2(a) shows the average value

of the assigned MCS, repetition and tone in different zones. It is important to note that, the

TABLE I: Simulation parameters

Parameter Value

Number of UE 100 - 600

UEs distribution random

Propagation model Okumura-Hata propagation model (Open area)

Hybrid building propagation model (Urban)

Frequency Band DL: 925 MHz, UL: 880 MHz

Tx Power eNodeB: 46 dBm, UE: 20 dBm

Packet Size 12 bytes

# Runs 100 runs

Inter-packet interval 10 seconds

Zone start (m) 0, 200, 600, 800, 1000, 2000, 2500, 2750, 3000

3500, 4000, 5000, 6000, 8000, 10000

Zone width (m) 200, 250, 500, 1000

6

farther the zone, the lower the value of SNR. We can observe that due to indoor deployment

in urban scenario the values of MCS, tone and repetitions are modiﬁed at closer distances. In

urban scenario, UE’s that are located inside buildings have very low values of SNR compared

to the open area and the MCS, repetition and tone are adapted more rapidly in order to improve

reliability.

Similarly, as shown in Fig. 2(b), the reduction in Packet Delivery Ratio (PDR) is steeper in

urban scenario. We can observe from the PDR graph that MCS provides good reliability until

zone 11 (4 km), in open areas scenario, while it starts to fail in zone 6 (2 km) in the urban

scenario. Tones start to fail at zone 14 (8 km) in the open areas and zone 9 (3 km) in urban.

Repetition also follows the same trend and achieves good reliability until zone 16 (10 km) in

open areas and zone 11 (4 km) in urban. Therefore, we can achieve good reliability until a

maximum distance of 10 km in open areas and 4 km in urban areas. Repetitions have the best

performance in both urban and open areas. However, an increase in repetitions has to be traded

off for a corresponding increase in the power consumption. Fig. 2(c) shows the average delay

or latency at different zones. We can observe that the delay starts to increase at a lower distance

for urban compared with open area. This clearly shows that the latency of transmission increases

as we move from open areas to urban areas. The delay follows the adapted value and increases

towards farther zones. Based on the above results, we can conclude that the improvement in

coverage comes at the cost of a higher delay. The link adaptation strategies illustrated above try

to adapt one of the features such as tone or MCS or repetitions. However, in practice, a more

useful solution will be to adapt all three of them in an optimal manner.

III. HYBRI D SOL UTIO N

The link adaptation strategies described in the previous section adapt only one of the three

coverage enhancement parameters, which result in saturation before achieving a good coverage.

In order to extend coverage, combining these parameters into a hybrid solution is inevitable.

When MCS, tones or repetitions are adapted to improve the reliability of a UE that has a poor

coverage, there is a corresponding increase in the transmission delay of the UE. Therefore, in

the hybrid solution, the values of tones, repetitions and MCS are evaluated in an optimized

manner such that the delay per user is minimal, while the reliability is not compromised. To

achieve this, we formulate an optimization problem, with transmission delay per user as the

objective function, and the reliability as the constraint. In addition to transmission delay, energy

7

consumption would also be an interesting objective for minimization. In this paper, however, we

only focus on the delay.

The delay of a UE is composed of synchronization delay, Random Access Channel (RACH)

delay and data transmission delay. In this paper, we only consider the data transmission delay,

as it is the delay that can stretch in time based on the amount of data. The uplink data

transmission delay per UE consists of Downlink Control Information (DCI), transmission of

data, and transmission and reception of the acknowledgment. The data transmission delay per

UE for the uplink (UL) transmissions can be written as [12],

Delay =T L × ⌈ Datalength

T BS (MCS, RU )⌉,(1)

where T L is the transmission latency, Datalength is the data size per user and T BS is the

transport block size. T L depends on the duration of a single transmission of DCI (tP DC CH ),

repetitions of control transmission (RLDC), downlink to uplink switching delay (tDU S ), du-

ration of a single subframe (tP U SC H ), the time factor (t), number of repetitions of the data

transmissions (RLUS) and time taken for acknowledgement (tACK ) as shown in Fig. 3. The

Narrowband Physical Uplink Shared Channel (NPUSCH) is used for uplink data transmission and

the Narrowband Physical Downlink Control Channel (NPDCCH) is used for downlink control

transmission. Hence, T L can be written as,

T L =RLDC ×tP DC CH +tDU S +RLU S ×t×tP US CH

+tUDS +RLU C ×tACK .(2)

The time factor tdepends on the number of tones assigned to the UE and can take values as 1, 2,

4, 8, and 32 for 12, 6, 3, 1 tones of 15 kHz spacing and 1 tone of 3.75 kHz spacing, respectively.

The acknowledgement and retransmissions are disabled to better analyze the performance of our

solution i.e., tU DS and tAC K are set to zero. For simplicity, we assume that there are no repetitions

in the DCI (RLDC = 0) and that the number of resource units is one (RU = 1).

Let us denote tP U SC H by K0,Datalength by K2and RLUS by r. Hence, we can rewrite

(1) as follows,

Delay = (K1+K0×r×t)⌈K2

T BS (m)⌉,(3)

where ris the number of repetitions, tis the time factor, K2is the datalength, K0and K1

are constants and T B S is the transport block size that depends on MCS denoted by m. The

8

Fig. 3: Uplink transmission latency in NB-IoT

table showing the relationship between MCS and TBS is speciﬁed in [1]. Considering the delay

expression given in (3), the optimization problem can be formulated as,

min

r,t,m Delay(r, t, m)

s. t. SNR ≥SNRTh (m)

r∈R, t ∈T, m ∈M,

(4)

where SNRTh(m)is the threshold SNR value that depends on MCS, denoted by m. MCS is an

integer value that belongs to the set M={0,1,2..., 12},r, representing repetitions, is an integer

value that belongs to the set R={1,2,4,8,16,32,64,128}and t, representing the time factor, is

an integer value that belongs to the set T={1,2,4,8,32}. In order to achieve good reliability,

the received SNR should be above SNRTh(m). The received SNR depends on propagation loss,

repetition and tone. The number of tones inﬂuence the transmission bandwidth which is given

by BW = 180 kHz/f, where fis the frequency factor. The frequency factor, f, can take values

as 1, 2, 4, 12, and 48 for 12, 6, 3, 1 tones of 15 kHz spacing and 1 tone of 3.75 kHz spacing,

respectively. The transmitted power spectral density (P S DT X ) depends on the frequency factor

(f), and is given by PT X /BW , where PT X is the transmitted power. Hence, the received SNR

is calculated as,

SNR =K3×f×r, (5)

where K3=PT X /(180kHz ×N0×P L),N0is the noise power spectral density and P L is the

pathloss.

The SNR obtained in (5) should be greater than a given threshold (SNRTh(m)) to achieve

a good reliability and low BLER. The value of SNRTh(m)depends on MCS and it can be

9

obtained from the NB-IoT BLER curves generated for each MCS. These BLER curves are

generated by performing link level simulations. Fig. 4 shows the generated BLER curves on

the uplink for different MCS values under Additive White Gaussian Noise (AWGN) channel.

Hence, SNRTh(m), for all m, can be obtained from Fig. 4 by setting the value of BLER to be

0.1.

-15 -10 -5 0 5 10 15

SNR (dB)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

BLER

MCS-0

MCS-1

MCS-2

MCS-3

MCS-4

MCS-5

MCS-6

MCS-7

MCS-8

MCS-9

MCS-10

MCS-11

MCS-12

BLER = 0.1

Fig. 4: BLER curves under different MCS values for AWGN channel.

The obtained SNRTh(m)needs to be met in order to guarantee that the packet is received at the

base station without any corruption. Using the expressions given in (3) and (5), the optimization

problem can be re-written as follows:

min

r,t,m

K2(K1+K0r t )

T BS (m)

s. t. K3×f×r≥SNRTh (m)

r∈R, t ∈T, m ∈M.

(6)

Note that the ceiling in (1) is dropped since it will not alter the outcome of the optimization. The

objective function given in (6) is non-convex and it is hard to solve it analytically without any

approximations. The optimization problem is solved using three methods, namely, the exhaustive

search, Lagrange and fsolve methods. In order to simplify the optimization problem (6) for

solving through the Lagrange and fsolve methods, some approximations are made. Furthermore,

the integer constraints on r,tand mare relaxed. In order to obtain these approximations, we

use curve ﬁtting function in MATLAB.

10

The ﬁrst approximation is done for T BS (m)which is the denominator of the objective

function. The obtained approximation is given by,

T BS (m) = a m2+b m +c, (7)

where a = 0.65, b=7.5, c=15.5 and the mean square error between the actual T B S(m)given in

[1] and the obtained approximation is equal to 20.

The second approximation is for SNRTh(m)in (6). The approximation of SNRTh(m)is derived

from BLER curves in Fig.4 and is given by,

SNRTh(m) = q1m3+q2m2+q3m+q4,(8)

where q1= 0.001055,q2= 0.007623,q3= 0.01359, and q4= 0.3615. The mean square error

between the actual and the approximated SNRTh (m)is 0.0047.

The ﬁnal approximation concerns the time and frequency factors. The objective function is

based on twhereas the SNR is based on f. Parameters fand tare both based on the number

of tones and are interrelated. For example, for a 15 kHz single-tone, tis equal to 8 and fis

equal to 12. Hence, we create an expression that relates fto tand it is given by,

f=p1t3+p2t2+p3t+p4(9)

where p1=−0.004994,p2= 0.2031,p3= 0.08811, and p4= 0.834. The mean square error

between the actual and the approximated function is 0.015.

Based on the above approximations, the optimization problem (6) can be re-written as,

min

r,t,m

K2(K1+K0r t )

a m2+b m +c

s. t. K3×p1t3+p2t2+p3t+p4×r≥

q1m3+q2m2+q3m+q4

0≤r≤128,0≤m≤12,0≤t≤32.

(10)

Based on the formulations of the optimization problem in equations (6) and (10), we solve the

optimization problem using different methods.

1) Lagrange: The method of Lagrange multipliers is used to solve the minimization problem

described in (6) and (10). In order to simplify the optimization problem and to have a closed-

form solution, we ﬁx the value of MCS, m. Thus, we search for the optimum values of rand

tfor a given value of m. Hence, in (10), since mis a constant, there is no need of using the

11

approximation of T B S(m)given in (7). Furthermore, we relax the integer constraint on rand

t. Based on (10) and these assumptions, the objective function and the constraints for a given

mare written as,

min

r,t,m

K2(K1+K0r t )

T BS (m)

s. t. K3rp1t3+p2t2+p3t+p4−SNRTh(m)≥0

0≤r≤128,0≤m≤12,0≤t≤32

The Lagrangian (L) is deﬁned as:

L=K2(K1+K0r t)

T BS (m)−λ K3rp1t3+p2t2+p3t+p4)

−λSNRTh(m),(11)

where r,tand Lagrangian multiplier λare the variables or unknowns. The partial derivatives

of the Lagrangian L are calculated for r,tand λas shown below:

∂L

∂r = 0,∂L

∂λ = 0,∂L

∂t = 0 (12)

K0K2t

T BS (m)−K3λp1t3+p2t2+p3t+p4= 0,(13)

K0K2r

T BS (m)−K3λ r 3p1t2+ 2 p2t+p3= 0,(14)

SNRTh(m)−K3rp1t3+p2t2+p3t+p4= 0 (15)

Solving (13) and (14) for tfor a given m, we get

2p1t3+p2t2−p4

3p1t2+ 2p2t+p3

= 0.(16)

From (16), we can see that tdepends only on the SNR. In order to get t, we solve 2p1t3+

p2t2−p4= 0 such that 3p1t2+ 2p2t+p36= 0. Solving these equations for the given parameters

pi, we get the following

t=−1.936,2.142,20.128 (17)

t6=−0.215,27.327 (18)

12

Out of these tvalues, the negative value is discarded and the only possible values are 20.128

and 2.142. We can obtain rby substituting the values of tin (15). Then, we search for the

integer combination of rand tthat gives minimal delay and a SNR value higher than SNRTh.

The value of mis chosen by performing an exhaustive search and obtaining the values of tand

rfor each value of m. The optimum solution is obtained by choosing the combination r,tand

mthat yield the lowest delay, while achieving good reliability, i.e., SNR≥SNRTh.

2) fsolve: The second method used to solve the optimization problem is fsolve, a MATLAB

function used to solve a system of multivariate non-linear equations. This method is based on

the approximated objective function (10).

3) Exhaustive search: The most straight-forward method to solve the optimization problem

is through an exhaustive search. For this method, we consider the optimization problem without

any approximations given by (6). This method is implemented by searching for all possible

combinations of m,rand t. Then, we select the combination that yield the smallest delay and

satisﬁes the SNR constraint.

IV. NUMER ICA L RESU LTS

The exhaustive, Lagrange and fsolve algorithms are ﬁrst implemented in MATLAB. The results

from the MATLAB implementation do not include network delays and are based on theoretical

models. The exhaustive search method is chosen as the base for evaluation since it is the most

accurate approach without any approximations. Table II shows the obtained mean square error

of fsolve and Lagrange methods compared with the exhaustive method. The Lagrange solution

has better accuracy than fsolve because less approximations are used. We can observe in Table II

that the Lagrange method is the fastest method with a speedup factor of about eight times over

the exhaustive method. This is achieved because the Lagrange method only iterates over the

value of m. fsolve is faster than exhaustive search but slower than the Lagrange method. This is

because fsolve is an iterative approach and it tries to ﬁnd the three unknowns, simultaneously.

In order to allocate tones, repetitions and MCS, the base station needs to perform the link

TABLE II: Accuracy and speed of fsolve and Lagrange

Method Mean square error Speed-up factor

fsolve 0.0018 1.5

Lagrange 0.0001028 8

13

Fig. 5: Delay per user for different approaches

adaptation at runtime for all the UE’s whenever there is a change in SNR. Hence, the speed of

the optimization algorithm is an important factor to be considered, while choosing the algorithm.

In order to evaluate our theoretical models for delay given in (1), the Lagrange and the exhaustive

approach are implemented in the NS-3 network simulator. The same random deployment scenario

described above for open areas in II-C is used to perform the simulations in NS-3.

Fig.5 depicts the delay obtained by adapting MCS, adapting tone, adapting repetitions and

adapting all the three parameters, i.e. hybrid optimization in NS-3. We should note that the

optimum values of the parameters in the hybrid solution are obtained using Lagrange method. The

delay obtained from NS-3 simulations of the Lagrange approach is is denoted by ’Lagrange (NS-

3)’ in Fig.5. The delay obtained from MATLAB using the theoretical expression in (1) optimized

using the Lagrange method is denoted in Fig.5 by ’Lagrange (model)’. We can observe that the

delay obtained using ’Lagrange (model)’ and ’Lagrange (NS-3)’ are similar. This conﬁrms that

the expression of the delay in (1) is correct. In the zoomed part of Fig.5, we can observe that

between zones 5 and 15, the hybrid solution, ’Lagrange (NS-3)’, gives the lowest delay among

the other methods and yields similar delay value at closer zones. Furthermore, the MCS, tone,

and repetition-only approaches show good performance with respect to the reliability up to a

maximum of 4 km, 8 km, and 10 km, respectively. However, through experiments, the hybrid

Lagrange approach provides good reliability up to a distance of 40 km in open areas scenario.

Thus, hybrid solution offers better network efﬁciency, lower delay or latency per user which

14

MCS Tone Rep Hybrid

Method

0

500

1000

1500

2000

2500

3000

Max no. of UE

Theoretical (Eqn.19)

NS-3 Simulation

Fig. 6: Scalability for reporting period of 10s.

means lower power consumption.

In addition to latency and power consumption, we also evaluate the network performance in

terms of scalability, which is the maximum number of users that can be supported in a network.

The maximum number of users that can be supported in a network is obtained from [12] and is

given by,

max NUE =⌊Reporting P eriod

DelayU E

⌋ × ⌊ NS C

SC U ⌋,(19)

where NSC is the total number of subcarriers available for allocation, DelayU E is the average

delay per user obtained in (1), and SCU is the number of subcarriers allocated to one user.

The reporting period (Reporting P eriod) is assumed to be the same for all users. Fig. 6 depicts

the results obtained using NS-3 simulator and using the theoretical expression given in (19) for

the different aforementioned methods. Fig. 6 shows the maximum number of users that can be

supported when NSC is 24, i.e., number of RBs is two, and the reporting period is 10 s. We can

observe that the Lagrange or hybrid method has the highest maximum number of users, mainly

because it is optimized to achieve lower delay per user (DelayU E ). Furthermore, in tone and

hybrid approaches, resource allocation is performed in terms of subcarriers (SC) and multiple

users can share the same RB whereas, in repetition and MCS approaches, the resource allocation

is performed in terms of resource blocks (RB) and every user is allocated a minimum of one

RB (12 SC). This means that the subcarrier per user (SCU) is ﬁxed to 12 in these approaches,

resulting in a lower maximum number of users than the tone and hybrid approaches. In the tone

and hybrid approaches, there is a difference between the NS-3 and the theoretical results because

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it is difﬁcult to simulate beyond 600 users in NS-3 due to memory and processing constraints.

V. CONC LUS ION

In this paper, we describe an implementation of uplink coverage enhancement methods of NB-

IoT in NS-3 simulator. We evaluate the performance of tones, repetitions and MCS with respect

to reliability and latency. We show that, an improvement in reliability at longer ranges comes at

the cost of a corresponding increase in latency. In order to achieve improved coverage and lower

latency, we propose a hybrid optimization strategy with latency as the objective function and

SNR as the constraint. We propose and implement three optimization methods the exhaustive

search, fsolve and Lagrange methods and we evaluate them based on accuracy and speed. We

show that the Lagrange method outperforms the other two methods in terms of execution speed

and yields the same latency as the exhaustive method. We implement the Lagrange method in

the NS-3 simulator and verify our optimization formulation. Through numerical results, we show

that the Lagrange method for hybrid link adaptation is eight times faster than the exhaustive

search approach and yields similar latency. Furthermore, it achieves a range of 40 km for open

areas and has better scalability than optimized tone, optimized repetition and optimized MCS

approaches.

VI. ACKNOWLEDGMENT

This work was partially funded by the Flemish FWO SBO S004017N IDEALIoT (Intelligent

DEnse And Long range IoT networks) project and the SCOTT project (SCOTT (www.scott-

project.eu) has received funding from the Electronic Component Systems for European Lead-

ership Joint Undertaking under grant agreement No 737422. This Joint Undertaking receives

support from the European Unions Horizon 2020 research and innovation programme and

Austria, Spain, Finland, Ireland, Sweden, Germany, Poland, Portugal, Netherlands, Belgium,

Norway).

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